A cyclist rides down a long straight road at a velocity (in m/min) given by v (t) = 400-20t, for 0≤t≤10, where t is measured in minutes.

A. How far does the cyclist travel in the first 5 min?

B. How far does the cyclist travel in the first 10 min?

C. How far has the cyclist traveled when her velocity is 250 m/min?

A. 1,500m

B. 2000m

C. 1875m

Step-by-step explanation:

A. Here, we simply substitute the value of t in the equation.

t = 5min

V (t) = 400 - 20t

= 400 - 20 (5)

= 400 - 100 = 300m/min

Now we know that distance = speed * time = 300 * 5 = 1,500m

2. Substitute t = 10

V = 400 - 20 (10) = 400 - 200 = 200m/min

Distance = speed * time = 200 * 10 = 2000m

3. Here we need to calculate time

Rearranging the equation:

20t = 400 - V (t)

20t = 400 - 250

20t = 150

t = 150/20 = 7.5min

Distance traveled = 250 * 7.5 = 1875m